Question: Solve the following linear programming model graphically: Maximize Z = 5x 1 + 8x 2 Subject to 3x 1 + 5x 2 ≤ 50 2x

Solve the following linear programming model graphically:

Maximize Z = 5x  1   + 8x  2 

Subject to

3x  1   + 5x  2   ≤ 50

2x  1   +4x  2    ≤ 40

x  1   ≤ 8

x  2   ≤ 10

x  1  , x  2   ≤ 0

Shade the feasible region.

What are the extreme points? Give their (x1, x2)-coordinates.

Plot the objective function on the graph to demonstrate where it is optimized.

What is the optimal solution?

What is the objective function value at the optimal solution?

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